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Given:
- \( DE = x - 4 \)
- \( EF = 2x + 5 \)
- \( DF = 4x - 8 \)

Since point \( E \) is between \( D \) and \( F \), we have:
\[
DF = DE + EF
\]
Substitute the given values:
\[
4x - 8 = (x - 4) + (2x + 5)
\]
Simplify the right side:
\[
4x - 8 = x - 4 + 2x + 5
\]
Combine like terms:
\[
4x - 8 = 3x + 1
\]
Subtract \( 3x \) from both sides to isolate \( x \):
\[
4x - 3x - 8 = 1
\]
\[
x - 8 = 1
\]
Add 8 to both sides:
\[
x = 9
\]

Now that we have \( x = 9 \), we can find the lengths of each segment:

1. **\( DE \):**
   \[
   DE = x - 4 = 9 - 4 = 5
   \]

2. **\( EF \):**
   \[
   EF = 2x + 5 = 2(9) + 5 = 18 + 5 = 23
   \]

3. **\( DF \):**
   \[
   DF = 4x - 8 = 4(9) - 8 = 36 - 8 = 28
   \]

### Answer:
The lengths of the segments are:
- \( DE = 5 \)
- \( EF = 23 \)
- \( DF = 28 \)

Would you like further clarification on this solution, or have any other questions?

Here are 5 related questions you might be interested in:
1. How do you set up an equation when a point lies between two other points?
2. What happens if the value of \( x \) in such problems turns out to be negative?
3. How do you find the midpoint of a segment given the endpoints?
4. How do you apply the segment addition postulate in different geometric problems?
5. What are the properties of line segments in geometric figures?

**Tip:** Always double-check each step when solving equations involving segments to ensure accuracy.

Point E is between points D and F. If DE = x - 4, EF = 2x + 5, and DF = 4x - 8, find the length of all segments.

Solve a problem where point E is between points D and F, with algebraic expressions given for segments DE, EF, and DF. Learn to apply the Segment Addition Postulate and algebraic methods to find the lengths of all segments.

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